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We show that the interaction constant governing the long-rangeelectron-electron interaction in a quantum wire coupled to two reservoirs andcapacitively coupled to a gate can be determined by a low frequencymeasurement. We present a self-consistent, charge and current conserving theoryof the full conductance matrix. The collective excitation spectrum consists ofplasma modes with a relaxation rate which increases with the interactionstrength and is inversely proportional to the length of the wire. Theinteraction parameter is determined by the first two coefficients of theout-of-phase component of the dynamic conductance measured at the gate.Comment: 4 pages, LaTeX, 2 figure

Interaction Constants and Dynamic Conductance of a Gated Wire